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# Extended F-expansion Method and Its Application to the Variable-coefﬁcient Fractional Nonlinear Schro¨dinger Equation

*Proceedings of 2024 International Conference on Machine Learning and Intelligent Computing*, PMLR 245:297-307, 2024.

#### Abstract

In this paper, under the deﬁnition of conformable fractional derivatives, we use the extended Fexpansion method and obtain the exact solution of the variable-coefﬁcient factional nonlinear Schrodinger equation (FNLSE), including rational function solutions and Jacobi elliptic function solution. When the mode m of these solutions tends to 1 and 0, the hyperbolic function solution, triangular function solution, and light and dark solitary wave solution are obtained. The correlation diagram of the exact solution is plotted, and the effect of different parameters on the solution structure is deeply analyzed. By selecting a large number of parameters and comparing the graphical analysis of different solutions obtained using this method, we have identiﬁed properties related to the nonlinear Schro¨dinger equation with variable coefﬁcients and summarized relevant theorems.